Q:

9.4 The heights of a random sample of 50 college stu- dents showed a mean of 174.5 centimeters and a stan- dard deviation of 6.9 centimeters. (a) Construct a 98% confidence interval for the mean height of all college students. (b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centime- ters?

Accepted Solution

A:
Answer:  a) (176.76,172.24), b) 0.976.Step-by-step explanation:Since we have given that Mean height  = 174.5 cmStandard deviation = 6.9 cmn = 50we need to find the 98% confidence interval.So, z = 2.326(a) Construct a 98% confidence interval for the mean height of all college students.[tex]x\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=(174.5\pm 2.326\times \dfrac{6.9}{\sqrt{50}})\\\\=(174.5+2.26,174.5-2.26)\\\\=(176.76,172.24)[/tex](b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centime- ters?Error would be [tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{6.9}{\sqrt{50}}\\\\=0.976[/tex]Hence, a) (176.76,172.24), b) 0.976.